Problem: Let $m=5x-2$. Which equation is equivalent to $(5x-2)^2+35x-14=-12$ in terms of $m$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $m^2+7m-2=0$ (Choice B) B $m^2-7m+12=0$ (Choice C) C $m^2-7m-2=0$ (Choice D) D $m^2+7m+12=0$
We are asked to rewrite the equation in terms of $m$, where ${m}={5x-2}$. In order to do this, we need to find all of the places where the expression ${5x-2}$ shows up in the equation, and then substitute ${m}$ wherever we see them! For instance, note that $35x-14=7({5x-2})$. This means that we can rewrite the equation as: $(5x-2)^2+35x-14=-12$ $({5x-2})^2+7({5x-2})=-12$ [What if I don't see this factorization?] Now we can substitute ${m}={5x-2}$ : $({m})^2+7({m})=-12$ Finally, let's manipulate this expression so that it shares the same form as the answer choices: ${m}^2+7{m}+12=0$ In conclusion, $m^2+7m+12=0$ is equivalent to the given equation when $m=5x-2$.